Finite Group Databasebeta

← #16818524

Subgroups — #16818524

Order 3712.

208 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 49 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14271758C211yesmaximal, characteristic
2#14271499C211yesmaximal, characteristic, complemented
3#14271479C211yesmaximal, characteristic
4#14271103C211yesmaximal, characteristic, complemented
5#14270899C211yesmaximal, characteristic, complemented
6#14270888C211yesmaximal, characteristic, complemented
7C29×#327C211yesmaximal, characteristic
8C29×#121C2211yescharacteristic
9#11745297—21no—
10#11745297—21no—
11D4×Dic29—21no—
12C2×C4⋊Dic29C2211yescharacteristic
13#11745286C2211yescharacteristic
14C2×#90779C2211yescharacteristic
15#11745251—21no—
16#11745241—21no—
17#11745240—21no—
18C29×C22⋊C8C2211yescharacteristic
19C29×#95C2211yescharacteristic
20#11745180—21no—
21#11745179—21no—
22#11745179—21no—
23C22⋊#6597C2211yescharacteristic
24#11745166—21no—
25#11745164—21no—
26#11745156—21no—
27C2×D4×C29—21no—
28C2×D4×C29D411yescharacteristic
29C22×C4×C29—21no—
30C22×C4×C29C2311yescharacteristic
31C22×Dic29—21no—
32C22×Dic29—21no—
33C22×Dic29D411yescharacteristic
34C22×Dic29D411yescharacteristic
35C2×Dic58D411yescharacteristic
36C2×C8×C29—21no—
37C4⋊C4×C29D411yescharacteristic
38C22⋊C4×C29—21no—
39C22⋊Dic29—21no—
40C22⋊Dic29—21no—
41C22⋊Dic29—21no—
42C22⋊Dic29—21no—
43C4⋊Dic29—21no—
44C4⋊Dic29—21no—
45C4⋊Dic29—21no—
46C4⋊Dic29D411yescharacteristic
47#90779—21no—
48#90779—21no—
49#90779—21no—
50#90779—21no—
51#90779—21no—
52C4×Dic29—21no—
53C2×#6597—21no—
54C23×C29—21no—
55C23×C29C2×D411yescharacteristic
56D4×C29—41no—
57D4×C29—41no—
58D4×C29—41no—
59C2×C4×C29—21no—
60C2×C4×C29—41no—
61C2×C4×C29—41no—
62C2×C4×C29—41no—
63C2×C4×C29—41no—
64C2×C4×C29C2×D411yescharacteristic
65C2×C4×C29C2×D411yescharacteristic
66C2×Dic29—21no—
67C2×Dic29—21no—
68C2×Dic29—21no—
69C2×Dic29—21no—
70C2×Dic29—21no—
71C2×Dic29—21no—
72C2×Dic29—41no—
73C2×Dic29—42no—
74C2×Dic29—41no—
75C2×Dic29—81no—
76Dic58—41no—
77C8×C29—41no—
78#6597—41no—
79#1615—291nomaximal, Sylow
80C22×C29—21no—
81C22×C29—21no—
82C22×C29—41no—
83C22×C29—41no—
84C22×C29—41no—
85C22×C29#12011yescharacteristic
86C22×C29#13511yescharacteristic
87C22×C29#13711yescharacteristic
88C4×C29—21no—
89C4×C29—21no—
90C4×C29—41no—
91C4×C29—81no—
92Dic29—41no—
93Dic29—41no—
94Dic29—41no—
95Dic29—41no—
96Dic29—81no—
97#539—291no—
98#484—291no—
99#481—291no—
100#400—291no—
101#328—291no—
102#327D2911yescharacteristic
103#324—291no—
104C2×C29—21no—
105C2×C29—21no—
106C2×C29—81no—
107C2×C29#45211yescharacteristic
108C2×C29#45411yescharacteristic
109C2×C29#45811yescharacteristic
110#126—581no—
111#125—581no—
112#123—581no—
113#123—581no—
114C22⋊Q8—291no—
115C22⋊Q8—581no—
116#121C2×D2911yescharacteristic
117C4×D4—581no—
118C2×C4⋊C4—291no—
119C2×C4⋊C4—291no—
120#107—581no—
121#106—581no—
122#103—581no—
123#102—581no—
124C22⋊C8—291no—
125C22⋊C8C2×D2911yescharacteristic
126#95—581no—
127#95—581no—
128#95C2×D2911yescharacteristic
129C29#161511yescharacteristic, complemented, Sylow
130C2×Q8—291no—
131C2×D4—21no—
132C2×D4D11611yescharacteristic
133C22×C4—21no—
134C22×C4—291no—
135C22×C4—291no—
136C22×C4—581no—
137C22×C4—581no—
138C22×C4C22×D2911yescharacteristic
139C2×C8—21no—
140C2×C8—581no—
141C4⋊C4—291no—
142C4⋊C4—581no—
143C4⋊C4—581no—
144C4⋊C4—581no—
145C4⋊C4—581no—
146C4⋊C4—581no—
147C4⋊C4—581no—
148C4⋊C4—581no—
149C4⋊C4—581no—
150C4⋊C4D11611yescharacteristic
151C22⋊C4—21no—
152C22⋊C4—581no—
153C22⋊C4—581no—
154C22⋊C4—581no—
155C22⋊C4—581no—
156C42—581no—
157C23—21no—
158C23D4×D2911yescharacteristic
159Q8—1161no—
160D4—41no—
161D4—41no—
162D4—41no—
163C2×C4—21no—
164C2×C4—41no—
165C2×C4—41no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—581no—
169C2×C4—581no—
170C2×C4—581no—
171C2×C4—581no—
172C2×C4—581no—
173C2×C4—581no—
174C2×C4—1161no—
175C2×C4—1162no—
176C2×C4—1161no—
177C2×C4—2321no—
178C2×C4C2×D11611yescharacteristic
179C2×C4D4×D2911yescharacteristic
180C8—41no—
181C8—1161no—
182C22—21no—
183C22—21no—
184C22—41no—
185C22—41no—
186C22—41no—
187C22#1174524411yescharacteristic
188C22#1174527411yescharacteristic
189C22#1174527711yescharacteristic
190C4—21no—
191C4—21no—
192C4—41no—
193C4—81no—
194C4—1161no—
195C4—1161no—
196C4—1161no—
197C4—1161no—
198C4—2321no—
199C2—21no—
200C2—21no—
201C2—81no—
202C2#1427132611yescharacteristic
203C2#1427133711yescharacteristic
204C2#1427135411yescharacteristic
subgroupG/H
centerC22#11745244
commutator, cosocleC22×C4×C29C23
FrattiniC22×C4C22×D29
FittingC29×#327C2
socleC22×C29#120
prime radicalC29×#121C22
hypercenter#327D29
hypocenterC29#1615
LCSG ▷ C22×C4×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #14271499C2semidirect
4. #14271103C2semidirect
5. #14270899C2semidirect
6. #14270888C2semidirect
129. C29#1615semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#142717582
#142714992
#142714792
#142711032
#142708992
#142708882
C29×#3272
#161529